My '58 Plymouth overheats in about 5 to 10 mile in normal traffic (max speed of 50 mph).
After that the temp gauge stays a little bit (not much) under the maximum mark.
If the weather is hot, or if I'm in heavier traffic, it might even let some cooling fluid out from the overheating bypass on the radiator.
It always did overheat, since the restoration was done, 2 years ago.

Now for some hard data :
- my engine is a 1958 standard 318 V8 that was fitted with the dual quad carbs and the corresponding camshaft
- it was internally rebuilt by a mechanic
- I had some hard time starting the engine after restoration, as it was very (and I mean very) sensitive on the dissy position (and I never understood why)
- The actual advance is unknown, since I don't have degree positions on the crankshaft pulley
- The spark plugs are Champion RJ12YC
- The radiator was cleaned and tested by a professional, although that was 8 years ago
- I run a standard modern cooling fluid
- Upon rebuilding the engine, I found a great deal of rust behind the freeze plugs. That rust was vacuumed out at the time.
- My cooling circuit runs without a thermostat, but I warn you that I'm scientifically convinced this is not the culprit.

Since then, here's what I've done :
- Checked my spark plugs : they are covered with black soot, and that would indicate too rich a mixture, but I don't believe this is related
- Reverse flushed the radiator : there was some rust dust in it and some traces of scale, although nothing major.
- Reverse flushed the engine block : nothing, clear liquid (but I did not open the lower drain bolts)
- Replace the water pump with a high flow Flowkooler one
- Improved the belt tension
- I dit find some rust in both hoses from the pump to the radiator (dust in the upper hose, small to medium specks in the lower hose)

Also, the water doesn't seem to be moving very much as you stated. It is possible that the left side of your radiator is partially plugged so that all the flow is going toward the right side. Get an infrared thermometer to test how hot each part of the radiator is and see if there is a cold spot somewhere. If you find one, the radiator is likely partially plugged up. You can also try squeezing the upper hose to see if the flow changes at all. If not, there is definitely a significant blockage, or the vanes on the pump are not working properly.

Did they degree in your camshaft when you had the motor rebuilt? If not, it is possible that your cam is advanced, causing some overheating issues and difficult timing issues.

When I squeeze the upper hose, nothing happens on the flow of the cooling liquid (which moves slowly from right to left when looking from the front). I also think about a radiator obstruction, although I reverse flushed it (but with low pressure water). I do have an infrared thermometer, I'll do the temperature mapping as soon as I can.

In the meantime, I checked my timing. I placed on the pulley ink marks at 10° and 20° as best as I could (accuracy not fully guaranteed but still).
At idle, I'm exactly on the 10° mark. At higher rpm it moves to 20° and upward ...

The FSM says it should be 10° for a regular 318, and 8° for the dual quad Fury. That is where the hybrid status of my engine kicks in. Because I do not have the heads of a true V800 engine, therefore my compression ratio is 9.0:1 instead of 9.25:1. But I do have the correct camshaft. So the question is : what is the correct advance timing ?

Years ago I had a 57 Fury that I installed a 60 361HP in. I used a stock big block radiator and at first removed the thermostat because of a mismatch between the temp. gauge and sender (thought it was overheating). I could idle all day in hot weather and it would never run hot but 15 minutes at highway speed and it would overheat. Tried everything, rad. was so clean inside it was shiny brass, finally reinstalled the thermostat and problem immediately ended. Have heard various theories through the years, pump cavitation, water flowing through the heads too fast to transfer the heat, whatever the reason, I am sure it overheated without the thermostat and not with it installed. Sorry for the long story. From your heat diagram, if you are sure your rad. is not partially plugged, maybe the water is flowing through too fast to transfer the heat? What would it hurt to install the thermostat and try it?

Of course it won't hurt to try a thermostat.
And I'm even willing to do it, for the sake of trying everything.

But it does not make sense.
The thermostat has only one purpose : keep the cooling circuit closed at startup to better heat up the engine.
And after a certain temperature, it opens so the fluid can be cooled by the radiator. And that's it.

I've read and heard theories about the fluid speed, and the fact that it would be slowed down by a thermostat, thus insuring a better cooling.
But that's bulls**t. Because the engine needs for cooling are measured by a capacity of the fluid to absorb calories.
And in the end, a lot of hotter fluid is way better than less cooler fluid, because the total of calories absorbed is bigger.
It's Physics 101.

But don"t take my words for it : https://www.flowkoolerwaterpumps.com/blogs/cooling-resources/doesnt-...
And if you want to skip the long read : "Simply put, you have a far better chance of keeping your cool with greater flow rate
through your heat exchanger and exiting the system than holding it in your heat exchanger while generating heat in your engine block."

But please, let's not hijack this thread to make a pro vs con thermostat issue. I'll try the thermostat, I promise
Let's stay on track.

At the risk of starting an ugly battle, infrared thermometers are less reliable than a contact thermometer, the surface being scanned will affect the readings.

And, you can quote all the blogs in existence, but the debate about the thermostat's purpose and the effectiveness of flow rate will continue based solely on anecdotal experience and fake science. IOW, both sides will claim their side is supported by Physics 101. Try a thermostat, then you'll know for sure.

I didn't want to start a fight but I KNOW for a fact my engine overheated at highway speed without a thermostat and never did again with it installed. Now you try to explain it with your science and flow rates to a person who is college educated and has been a mechanic for over 50 years. You may call it anecdotal but if it barks like a dog, wags its tail like a dog, and looks like a dog, I call it a dog.
I don't want to hijack your thread but you said you have tried everything else and you asked for suggestions.

"But it does not make sense.
The thermostat has only one purpose : keep the cooling circuit closed at startup to better heat up the engine.
And after a certain temperature, it opens so the fluid can be cooled by the radiator. And that's it."

It makes perfect sense. It works exactly as you said except for 2 missing parts. First, once fully open, it still is a restriction to coolant flow and secondly, it
works on a thermal spring which regulates coolant flow to the temperature, so it not open "and that's it" , it actually opens and closes a little depending on
whats going on with the temperature of the coolant.

The coolant needs time to absorb the heat from the engine and time to dissipate that heat to the radiator and then to the air, this is why the thermostat is a
restriction, to slow the coolant even at fully open. Some coolants work better than others (comparing water to general coolant) but normally in an original
cooling system, overheating is caused by a severe blockage (stuck thermostat, sucked in hoses, debris/rust blocking radiator cores) water pump not
working (impeller fallen off/blades rusted off, not spinning) no air flow (self explanatory) over stressed engine components (high power use for sustained periods or
high performance use) or the classic, no or low coolant

The old trick of removing the thermostat to stop a car overheating normally simply means the system is severely blocked or the water pumps had it
and removing the thermostat has allowed a bit more coolant to flow, which at highway speeds, then becomes to much and the coolant doesn't get time to pick up and dissipate the heat

It may also have to do with the radiator too. If yours is the stock 2 core; 2 cores have a tendency to get hot. If you think about replacing it (not saying you should), I'd go with a 3 or a 4 core radiator. Your motor will run under 200 all day long. If they can cool a big block, they'll for sure cool that 318.

Also, I know some don't like flex fans for the added wind noise, but what is the great thing about them is they flex when your speed and RPM increases, doing so, allowing more air flow to be directed at the motor. More air = cooler motor.

Also, I know some don't like flex fans for the added wind noise, but what is the great thing about them is they flex when your speed and RPM increases, doing so, allowing more air flow to be directed at the motor. More air = cooler motor.

That is not the purpose of a flex-fan and that is not what they do and you can't cool a water-cooled engine that way. Solely the water (radiator) cools the engine.

At first, I think I'll flush again the radiator, this time out of the car, because it looks indeed like there's some blockage.
Secondly, I'll drain the lower part of the engine block, opening the two screw plugs.

I learned a long time ago about the only time you should take out the thermostat is when your racing. As far as I'm concerned the factory engine designers are pretty smart and every engine builder after market puts in a thermostat. To purposely remove the facoty intent is to alter intended means of operation. Ok engine rebuilt or just cleaned up? What about the heater core? Was it boiled out or replace? The same gunky rust you found hiding in the coolant galleys is stuck in the heater core. Rememer it shares the same water the engine and the big out front radiator use. And again a removed radiator shroud? The shroud condenses and forces the concentrated air flow through the radiator. If nothing else just put on a set of electric fans.

Check your cooling specs in your FSM.
I took for granted one of my cars should use a 180* thermostat and ran one for several years.
I happened to catch in the cooling specs that the thermostat "starts to open at 157* and is fully open at 180*".
I switched to a 160* thermostat and it shows it running cooler on the factory gauge.
I verified the start to open temps as the temps stamped on the thermostats and fully open was +20* .

Check your cooling specs in your FSM.
I took for granted one of my cars should use a 180* thermostat and ran one for several years.
I happened to catch in the cooling specs that the thermostat "starts to open at 157* and is fully open at 180*".
I switched to a 160* thermostat and it shows it running cooler on the factory gauge.
I verified the start to open temps as the temps stamped on the thermostats and fully open was +20* .